Write an equation of a line that passes through (-12, -14) with slope 6.
A.y = 6x - 12
B.(y + 14) = 6(x + 12)
C.(y + 12) = 14(x + 6)
I've tried so many different ways to find this answer but can't. Please help me and please show me how you got it. I don't want you to just tell me the answer I want you to show me how to find others like this one. Thank you.
y = m x + b
m = slope
in tis case:
m = 6
x = - 12
y = - 14
y = 6 x + b
- 14 = 6 * ( - 12 ) + b
- 14 = - 72 + b
- 14 + 72 = b
58 = b
b = 58
y = m x + b
y = 6 x + 58
y = 6 x + 58
OR
y + 14 = 6 x + 58 + 14
y + 14 = 6 x + 72
y + 14 = 6 ( x + 12 )
Ansver B is correct
Proof:
y + 14 = 6 ( x + 12 )
- 14 + 14 = 6 ( - 12 + 12 )
0 = 6 * 0
0 = 0
If you have a point (a,b) and the line has slope of m, then the equation is
y-b = m(x-a)
the equation in B) fits that pattern exactly.
To find the equation of a line that passes through a given point (-12, -14) with a given slope of 6, we can use the point-slope form of the equation of a line and substitute the given values.
The point-slope form of the equation of a line is given by: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
In this case, we have (x1, y1) = (-12, -14) and m = 6. Substituting these values into the point-slope form, we get:
y - (-14) = 6(x - (-12))
Simplifying the equation:
y + 14 = 6(x + 12)
Now let's compare this simplified equation with the options given:
A. y = 6x - 12
B. (y + 14) = 6(x + 12)
C. (y + 12) = 14(x + 6)
We notice that option B matches our equation.
So, the correct equation that represents a line passing through (-12, -14) with a slope of 6 is:
(y + 14) = 6(x + 12).
If you encounter similar questions in the future, remember to use the point-slope form of the equation of a line and substitute the given point and slope values.